Problem: Ashley is 3 times as old as Gabriela. Fifteen years ago, Ashley was 8 times as old as Gabriela. How old is Gabriela now?
Answer: We can use the given information to write down two equations that describe the ages of Ashley and Gabriela. Let Ashley's current age be $a$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $a = 3g$ Fifteen years ago, Ashley was $a - 15$ years old, and Gabriela was $g - 15$ years old. The information in the second sentence can be expressed in the following equation: $a - 15 = 8(g - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to use our first equation for $a$ and substitute it into our second equation. Our first equation is: $a = 3g$ . Substituting this into our second equation, we get: $3g$ $-$ $15 = 8(g - 15)$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $3 g - 15 = 8 g - 120$ Solving for $g$ , we get: $5 g = 105.$ $g = 21$.